D. Divsalar, H. Jin and R. J. McEliece, "Coding theorems for 'turbo-like' codes", Proc. 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....be adjusted in such a manner that there are very few (or no) insertions. Thus, using a good erasure correcting code, one can deal with insertions deletions without significant decline in original embedding rate. Reed Solomon codes [8] have been used for ET scheme and Repeat Accumulate codes [9] have been used for the SEC scheme as described in following sections. B. Reed Solomon (RS) coding for ET scheme Reed Solomon codes [8] are MDS codes, such that any k coordinates of an (n,k) RS code can be treated as message positions. In other words, the k message symbols can be decoded even if ....

....scheme, where we consider powerful binary codes that are well matched to AWGN channels, as well as close to optimal for dealing with erasures. C. Repeat accumulate (RA) coding for SEC scheme Any turbo like code that operates close to Shannon limit could be used with SEC scheme. We used RA codes [9] in our experiments because of their simplicity of decoding and near capacity performance for erasure channels [10] A rate 1 q RA encoder involves q fold repetition, pseudorandom interleaving and accumulation of the resultant bit stream. Decoding is performed iteratively using the sum product ....

H. Jin, D. Divsalar, and R. J. McEliece, "Coding theorems for turbo-like codes," in 36th Allerton Conference on Communications, Control, and Computing, Sept. 1998, pp. 201--210.

....after 8000 block transmissions) In my experience RA codes with smaller block lengths make more undetected errors. I m going to investigate further these undetected errors (which sometimes correspond to codewords and sometimes to near codewords) Discussion The Divsalar, Jin and McEliece paper [1] contains graphs for up to 30 iterations. Histogram (a) above shows that roughly 50 of the decodings in my simulation at 0.65dB took more than 30 iterations, with a small but substantial number taking more than 60 iterations. So if you ran the old fashioned decoder for a whopping twice as long, ....

D. Divsalar, H. Jin, and R. J. McEliece. Coding theorems for 'turbo-like' codes. 1998.

....apply Theorem 4. 1 to three families of binary code ensembles: 1) The Shannon ensemble, consisting of all linear codes of rate R; 2) the GMlager ensemble, consisting of (j, k) low density parity check codes; and (3) the ensemble of Repeat Accumulate codes introduced by DivsMar, Jin and McEliece [2]. In the case of the Shannon ensembles, we show that our method yields thresholds identical to those implied by Shanon s theorem. Thus the typical sequence method, despite its suboptimMity, loses nothing (in terms of coding thresholds) for the Shannon ensemble. Finally, we compare our thresholds ....

....Theorem 4. 1 to three different ensembles of binaxy lineax codes: 1) The Shannon ensemble, consisting of all linear codes of rate R; 2) the Gallager ensemble, consisting of (j, k) low density parity check codes; ad (3) the ensemble of RepeatAccumulate codes introduced by Divsalax, Jin ad McEliece [2]. 5. The Shannon ensemble. For the set of random linear codes of rate R, we have (5.1, from which it follows via a routine calculation that (5.2) r(5) H(5) 1 R)log2. This function is shown for R = 1 3 in Figure 2. To apply Theorem 4.1 to the Shannon ensemble, 4 for a given rate R we ....

D. DIVSALAR, H. JIN, AND R. MCELIECE, "Coding Theorems for 'Turbo-Like' Codes." Proc. 1998 Allerton Conf., pp. 201-210.

....these codes. The recent overwhelming attention given to the bounding techniques for performance evaluation of codes is mainly due to the introduction of some near Shannon limit performing schemes. Turbo codes, invented by Berrou et al. 2] in 1993, Repeat Accumulate (RA) codes of Divsalar et al. [6], and Low Density Parity Check (LDPC) codes of Gallager [13] resurrected by MacKay et al. 21] in 1996 are the best examples. In addition to simulations, the aforementioned schemes can be analyzed using the union bound which is a very loose measure of performance for rates above the cuto rate of ....

D. Divsalar, H. Jin, and R. J. McEliece, \ Coding theorems for 'Turbo-like' codes," 1998.

....these codes. The recent overwhelming attention given to the bounding techniques for performance evaluation of codes is mainly due to the introduction of some near Shannon limit performing schemes. Turbo codes, invented by Berrou et al. 3] in 1993, Repeat Accumulate (RA) codes of Divsalar et al. [4], and Low Density Parity Check (LDPC) codes of Gallager [5] resurrected by MacKay et al. 6] in 1996 are the best examples. In addition to simulations, the aforementioned schemes can be analyzed using the union bound which is a very loose measure of performance for rates above the cuto rate of ....

D. Divsalar, H. Jin, and R. J. McEliece, \ Coding theorems for 'Turbo-like' codes," 1998.

....interesting to note from Property 2 that when the number of transmissions K = 2, P U (EK ) is independent of interleaver size N for precoded ISI channels. In other words, there is no coding gain for precoded ISI channels for the case K = 2. This result agrees with that for repeat accumulate codes [6] with repetition codes of length two. For the case of nonprecoded ISI channels, P U (EK ) increases as N increases. Thus, precoded ISI channels still outperform nonprecoded ISI channels in terms of P U (EK ) even when K = 2. So far, we have only considered time invariant ISI channels. We next ....

D. Divsalar, H. Jin, and R. J. McEliece, "Coding theorems for `turbo-like' codes," in Proc. 36th Allerton Conf. on Communication, Control, and Computing, pp. 201-210, Sept. 1998.

....or less) convolutional codes and even very simple repetition codes [15] are good outer code candidates to provide satisfactory performance. However, the construction of very high rate codes based on this concept poses a problem. The key problem here is that, from Benedetto et al. s results [16] [17], the outer code must have a minimum distance of at least 3 in order to obtain an interleaving gain. To obtain good high rate convolutional codes through puncturing, and in particular to maintain a dmin of 3 after puncturing, the original convolutional codes must have fairly long constraint ....

.... Further, we show that these codes can perform close to capacity limits by computing thresholds for these codes based on the tight upper bound on the word error rate (WER) due to Divsalar [4] A) Interleaving Gain From the results of Benedetto et al. [16] and Divsalar, Jin and McEliece [17], we know that for a general serial concatenated system with recursive inner code, there exists a threshold # such that for any E b N 0 #, the asymptotic word error rate is upper bounded by: UB w = O N # d o m 1 , 30) where d m is the minimum distance of the outer code and N is ....

[Article contains additional citation context not shown here]

D. Divsalar, H. Jin and R. J. McEliece, "Coding theorems for 'turbo-like' codes," Proc. 1998.

....be adjusted in such a manner that there are very few (or no) insertions. Thus, using a good erasure correcting code, one can deal with insertions deletions without significant decline in original embedding rate. Reed Solomon codes [8] have been used for ET scheme and Repeat Accumulate codes [9] have been used for the SEC scheme as described in following sections. B. Reed Solomon (RS) coding for ET scheme Reed Solomon codes [8] are MDS codes, such that any k coordinates of an (n,k) RS code can be treated as message positions. In other words, the k message symbols can be decoded even if ....

....to AWGN channels, as well as close to optimal for dealing with erasures. C. Repeat accumulate (RA) coding for SEC scheme Many turbolike codes such as low density parity check (LDPC) codes by Gallager, repeat accumulate (RA) codes and irregular repeat accumulate codes (IRA) by Divsalar et al. [9], 10] and certain others operate close to Shannon limit and can be used with SEC scheme. We used RA codes in our experiments because of their simplicity of decoding and near capacity performance for erasure channels [10] A rate 1 q RA encoder, as the name suggests, involves q fold repetition, ....

H. Jin, D. Divsalar, and R. J. McEliece, "Coding theorems for turbo-like codes," in 36th Allerton Conference on Communications, Control, and Computing, Sept. 1998, pp. 201-210.

....of Technology Pasadena, CA 91125 USA E m#364 hui, aam# d,rjm system#57146Tm h.edu Abstract: In this pa per we will introducea n ensemble of codes ca lled irregularrep eat accumulate (IRA) codes. IRA codesa# ea genera#ner]SJ7 of the repea#74J cumlua#6 codes introduced in [1],a#] a# such ha#c a na#ch a# linea#ne]J4 encodinga#g]SJ355] We sha# l provetha# on thebina#5 era#]J echa#JJ9] IRA codes ca n be decoded relia#57 in linea# time, using itera#er] sum product decoding,a# ra#SJ a#SJ8T a#SJ8 close tocha#T36 ca pa#J464 Asimila# resulta#u ea#S to ....

....finalp#al(4x has been solved, although researchers are very close on the AWGN channel and extremely close on the binary erasure channel. In thisp#i er, we will introduce a p#8ITxz(R class of codes called irregula# repea#43J cumula#] codes, which generalizes therep eat accumulate codes of [1]. After defining the codes in Section 2, and observing that they have asimp#z linear time encoding algorithm, in Section 3, using thep owerful Richarson Urbanke method [2] we willp#l ve rigorously that IRA codes solve the finalp#al(4x for the binary erasure channel. In Section 4, we will ....

[Article contains additional citation context not shown here]

D. Divsalar, H. Jin, and R. J. McEliece, "Coding theorems for `turbo-like' codes,"p#s 2012.

....apply Theorem 4. 1 to three families of binary code ensembles: 1) The Shannon ensemble, consisting of all linear codes of rate R; 2) the Gallager ensemble, consisting of (j; k) low density parity check codes; and (3) the ensemble of Repeat Accumulate codes introduced by Divsalar, Jin and McEliece [2]. In the case of the Shannon ensembles, we show that our method yields thresholds identical to those implied by Shannon s theorem. Thus the typical sequence method, despite its suboptimality, loses nothing (in terms of coding thresholds) for the Shannon ensemble. Finally, we compare our thresholds ....

....4. 1 to three different ensembles of binary linear codes: 1) The Shannon ensemble, consisting of all linear codes of rate R; 2) the Gallager ensemble, consisting of (j; k) low density parity check codes; and (3) the ensemble of RepeatAccumulate codes introduced by Divsalar, Jin and McEliece [2]. 5. The Shannon ensemble. For the set of random linear codes of rate R, we have A (n) h = n h 2 Gamman(1 GammaR) 5.1) from which it follows via a routine calculation that r(ffi) H(ffi) Gamma (1 Gamma R) log 2: 5.2) This function is shown for R = 1=3 in Figure 2. To apply ....

D. Divsalar, H. Jin, and R. McEliece, "Coding Theorems for `Turbo-Like' Codes." Proc. 1998 Allerton Conf., pp. 201--210.

No context found.

D. Divsalar, H. Jin and R. J. McEliece, "Coding theorems for 'turbo-like' codes", Proc. 1998.

No context found.

D. Divsalar, H. Jin, and R. J. McEliece, "Coding theorems for 'turbo- like' codes," in Proc. 1998.

No context found.

D. Divsalar, H. Jin, and R. J. McEliece, "Coding theorems for turbo-like codes," in 36th Allerton Conference on Communications, Control, and Computing, Sept. 1998, pp. 201--210.

No context found.

D. Divsalar, H. Jin, and R. J. McEliece, "Coding theorems for `turbolike ' codes," in Proc. 36th Annu. Allerton Conf. Communication, Control, and Computing, Monticello, IL, Sept. 1998, pp. 201--210.

No context found.

D. Divsalar, H. Jin, and R. J. McEliece, "Coding theorems for `turbo-like' codes," 36th Allerton Conference on Communications, Control, and Computing, Monticello, Illinois, pp. 201-210, 1998.

No context found.

D. Divsalar, H. Jin, and R. J. McEliece, "Coding theorems for turbo-like codes," in 36th Allerton Conference on Communications, Control, and Computing, Sept. 1998, pp. 201--210.

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R. J. McEliece, D. Divsalar, and H. Jin, "Coding theorems for `turbo-like' codes," in Proceedings of the 35 Control and Computing 1997.

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D. Divsalar, H. Jin, and R.J. McEliece, "Coding theorems for 'turbo-like' codes," in Allerton conf. on Communication, Control and Computing., Allerton (Il, USA), 1998, pp. 201-- 210.

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D. Divsalar, H. Jin, and R. J. McEliece, "Coding theorems for `turbolike ' codes," in Proc. 36th Allerton Conf. Communications, Control, and Computing, Urbana, IL, Sept. 23--25, 1998, pp. 201--210.

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Divsalar, D., Jin, H., and McEliece, R. J. Coding theorems for 'turbo-like' codes. In Proceedings of 36th Allerton Conference on Communication, Control, and Computing (Sept. 1998), pp. 201--210. 204

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D. Divsalar, H. Jin, and R. J. McEliece, \ Coding theorems for 'Turbo-like' codes," 1998.

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